As far as I understand, that should be the interpolated function. For example, if splines are used for the interpolation, then

g:=unapply(CurveFitting:-Spline([2,3,4,5],[-7,3.2,4.1,10.45],x),x):

If the PolynomialInterpolation is used, you should replace Spline with PolynomialInterpolation. See ?CurveFitting for other possible ways of interpolating in Maple. Without using the interpolated function the calculations can not be done with h=0.01 - table values are good only for h=0.5 and one doesn't need Maple to do that in this case, (3.2+7)/1=10.2 __________ Alec Mihailovs http://mihailovs.com/Alec/

As far as I understand, that should be the interpolated function. For example, if splines are used for the interpolation, then

g:=unapply(CurveFitting:-Spline([2,3,4,5],[-7,3.2,4.1,10.45],x),x):

If the PolynomialInterpolation is used, you should replace Spline with PolynomialInterpolation. See ?CurveFitting for other possible ways of interpolating in Maple. Without using the interpolated function the calculations can not be done with h=0.01 - table values are good only for h=0.5 and one doesn't need Maple to do that in this case, (3.2+7)/1=10.2 __________ Alec Mihailovs http://mihailovs.com/Alec/

Also, ExtremePoints can be used from Student:-Calculus1 package. For example,

f,r,a:=t->sqrt(1-2*r*cos(t)+r^2)+sqrt(1-2*r*cos(t-a)+r^2),1/2,Pi:

Student:-Calculus1:-ExtremePoints(f(t),t=-Pi..Pi);

                               Pi       Pi
                      [-Pi, - ----, 0, ----, Pi]
                               2        2

map(f,%);

                             1/2      1/2
                        [2, 5   , 2, 5   , 2]

evalf(%);

                [2., 2.236067977, 2., 2.236067977, 2.]

__________ Alec Mihailovs http://mihailovs.com/Alec/

Also, ExtremePoints can be used from Student:-Calculus1 package. For example,

f,r,a:=t->sqrt(1-2*r*cos(t)+r^2)+sqrt(1-2*r*cos(t-a)+r^2),1/2,Pi:

Student:-Calculus1:-ExtremePoints(f(t),t=-Pi..Pi);

                               Pi       Pi
                      [-Pi, - ----, 0, ----, Pi]
                               2        2

map(f,%);

                             1/2      1/2
                        [2, 5   , 2, 5   , 2]

evalf(%);

                [2., 2.236067977, 2., 2.236067977, 2.]

__________ Alec Mihailovs http://mihailovs.com/Alec/

The description of applyop can be found in its help page, ?applyop. Your example is just a double integral. One doesn't need dsolve to evaluate it. Using applyop, it can be done as

u:=1+sum((-1)^(i)*Heaviside(t-T[i+1]),i=1..n-1)+
sum((-1)^(i)*Heaviside(t-T[n+i]),i=1..n):

value(map[3](applyop,student[Doubleint],1,u,t,t))/M;

  /       /n - 1
  |  2    |-----
  | t     | \        i                               2
  |---- + |  )   (-1)  (1/2 Heaviside(t - T[i + 1]) t
  | 2     | /
  |       |-----
  \       \i = 1

                                               2
         - 1/2 Heaviside(t - T[i + 1]) T[i + 1]  - T[i + 1] (

        Heaviside(t - T[i + 1]) t - Heaviside(t - T[i + 1]) T[i + 1])

         \   /  n
         |   |-----
         |   | \        i                               2
        )| + |  )   (-1)  (1/2 Heaviside(t - T[n + i]) t
         |   | /
         |   |-----
         /   \i = 1

                                               2
         - 1/2 Heaviside(t - T[n + i]) T[n + i]  - T[n + i] (

        Heaviside(t - T[n + i]) t - Heaviside(t - T[n + i]) T[n + i])

         \\
         ||
         ||
        )||/M
         ||
         ||
         //

If you want to avoid using applyop or double integral for some reason, then you could just do your manipulations with dsolve for every term (1 and expressions inside sums) and then add them manually. _________ Alec Mihailovs http://mihailovs.com/Alec/

Very nice! At first I thought that it doesn't work in IE, but it started to work after restarting it. Probably, IE used cashed pages before restarting. __________ Alec Mihailovs http://mihailovs.com/Alec/

Sure it can be plotted using spacecurve or tubeplot,

plots[tubeplot]([cos(t),sin(t),t/2+3],t=0..10*Pi,radius=0.05,numpoints=300);

__________ Alec Mihailovs http://mihailovs.com/Alec/

Sure it can be plotted using spacecurve or tubeplot,

plots[tubeplot]([cos(t),sin(t),t/2+3],t=0..10*Pi,radius=0.05,numpoints=300);

__________ Alec Mihailovs http://mihailovs.com/Alec/

Magma creators put Magma calculator on their web site, Magma Calculator. Now it can be accessed from Maple using

Magma:=proc(x) 
local s,a,b;
uses StringTools, Sockets;
s:=Open("magma.maths.usyd.edu.au",80);
Write(s,cat("GET /calc/?input=",
            map((c->cat("%",c))@convert,convert(Squeeze(x),bytes),hex)[],
            " HTTP/1.0\n\n"));
a := "";
		b := Read(s):
		while b <> false do
			a := cat(a,b);
			b := Read(s):
		end do;
Close(s);
a[Search("--",a)..Search("Total",a)-1]
end:

For example,

Magma("Q:=GaloisField(35098201); P<x,y>:=PolynomialRing(Q,2); 
I:=ideal<P| y + (1+x^5+x^10), x^34 +1 >; Groebner(I); I;");

  "-------------------------------------

        Ideal of Polynomial ring of rank 2 over GF(35098201)
        Lexicographical Order
        Variables: x, y
        Dimension 0
        Groebner basis:
        [
            x + 33784728*y^33 + 15744019*y^32 + 14466235*y^31 + 14\
        937582*y^30 +
                9988153*y^29 + 24849537*y^28 + 13827463*y^27 + 108\
        51940*y^26 +
                25333828*y^25 + 29238403*y^24 + 35087366*y^23 + 31\
        85785*y^22 +
                12125255*y^21 + 11305600*y^20 + 713800*y^19 + 1188\
        2241*y^18 +
                23388419*y^17 + 12677392*y^16 + 20159861*y^15 + 31\
        143912*y^14 +
                33062327*y^13 + 11580433*y^12 + 10629964*y^11 + 14\
        094725*y^10 +
                12235446*y^9 + 20913610*y^8 + 23355486*y^7 + 34436\
        076*y^6 + 35026862*y^5
                + 12351747*y^4 + 6022820*y^3 + 34537573*y^2 + 9514\
        380*y + 16409093,
            y^34 + 34*y^33 + 561*y^32 + 5984*y^31 + 46376*y^30 + 2\
        78256*y^29 +
                1344904*y^28 + 5379616*y^27 + 18156204*y^26 + 1735\
        3055*y^25 +
                25833537*y^24 + 5312152*y^23 + 21881025*y^22 + 154\
        30534*y^21 +
                23145801*y^20 + 30861068*y^19 + 27872968*y^18 + 17\
        124952*y^17 +
                27873223*y^16 + 30858484*y^15 + 23140973*y^14 + 15\
        452362*y^13 +
                21951303*y^12 + 5362540*y^11 + 25762851*y^10 + 171\
        83633*y^9 +
                18014271*y^8 + 5332492*y^7 + 1357246*y^6 + 297330*\
        y^5 + 54791*y^4 +
                7854*y^3 + 748*y^2 + 34*y + 1
        ]

        "

__________ Alec Mihailovs http://mihailovs.com/Alec/

Another useful thing would be if a new version of Maple added a plotsetup(light) feature with plots displayed as gifs (or other small format, such as png, or maybe even svg) in the worksheet. That wouldn't allow usual manipulations with them, but worksheet size would be significantly smaller for worksheets with plots of a huge size as in the examples in this thread. __________ Alec Mihailovs http://mihailovs.com/Alec/

Beside (some) Maplesoft people posting here (from time to time), I prefer posting here for few other reasons as well. I like that it is moderated. I like that posts can be edited or even deleted. For example, being in a bad mood, I can write something about 'nuclear objects', but next morning I can delete that and pretend that nobody read it. Also, I like user pictures and Maple rating. I am missing Edwin Clark's, Robert Israel's, and Carl Love's (in alphabetical order) posts here though, as well as other experts' mentioned on my old Maple page posts. __________ Alec Mihailovs http://mihailovs.com/Alec/

Actually, I just realized that that could be done much more simple using power 1/2,

f:=n->(n^2)^(1/2);

for positive integers, with a simple modification for negative integers :) __________ Alec Mihailovs http://mihailovs.com/Alec/

Actually, I just realized that that could be done much more simple using power 1/2,

f:=n->(n^2)^(1/2);

for positive integers, with a simple modification for negative integers :) __________ Alec Mihailovs http://mihailovs.com/Alec/

icdf uses different integral, it starts from -infinity,

solve(int(1/sqrt(2*Pi)*exp(-t^2/2),t=-infinity..(x-mu)/s)=.95,x); 

                             3458.949665

Most tables use the same form of the integral as in icdf. Still, icdf can be used for the original problem with integral from -Z to Z as

stats[statevalf,icdf,normald[mu,s]](0.975);

                             3642.659003

Also, new Statistics package can be used,

Statistics:-InverseSurvivalFunction(Normal(mu,s),0.025);

                         3642.65900298649467

__________ Alec Mihailovs http://mihailovs.com/Alec/

icdf uses different integral, it starts from -infinity,

solve(int(1/sqrt(2*Pi)*exp(-t^2/2),t=-infinity..(x-mu)/s)=.95,x); 

                             3458.949665

Most tables use the same form of the integral as in icdf. Still, icdf can be used for the original problem with integral from -Z to Z as

stats[statevalf,icdf,normald[mu,s]](0.975);

                             3642.659003

Also, new Statistics package can be used,

Statistics:-InverseSurvivalFunction(Normal(mu,s),0.025);

                         3642.65900298649467

__________ Alec Mihailovs http://mihailovs.com/Alec/